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This paper mainly studies the limit behavior of Riemann solutions for the macroscopic production model with antiChaplygin gas. Firstly, we investigate the Riemann problem associated with this model. Three types of Riemann solutions are obtained: a combination of contact discontinuity and rarefaction wave( J1 + R2), a combination of contact discontinuity and shock wave( J1 + S2), and Dirac shock wave( δS). Secondly, the pressure vanishing limit of the macroscopic production model of the anti-Chaplygin gas is studied. As the perturbation parameter ε decreases to the parameter ε0, which is dependent only on the initial data, it is proved that the Riemann solution(J1 + S2) converges to the δS of the anti-Chaplygin gas state equation. Moreover, when ε eventually approaches 0, the δS converges to the δS of the transport equation. Additionally, it is proved that the Riemann solution(J1 + R2) converges to the vacuum solution of the transport equation. Finally, we present some representative numerical experimental results.
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Basic Information:
DOI：10.13568/j.cnki.651094.651316.2025.03.02.0001
China Classification Code:O175
Citation Information:
[1]He Weihua,Guo Lihui.The Asymptotic Limit of the Riemann Solution for the Macroscopic Production Model with Anti-Chaplygin Gas[J].Journal of Xinjiang University (Natural Science Edition in Chinese and English),2026,43(02):183-195.DOI:10.13568/j.cnki.651094.651316.2025.03.02.0001.
Fund Information:
新疆人才发展基金资助“流体动力学方程组的初边值问题”（XJRC-2025-KJ-PY-KJLJ-105）; 中央引导地方科技发展项目“非线性守恒律方程组的初边值问题”（ZYYD2026ZY11）
2026-03-15
2026-03-15